The glass structure and physical properties are reported for the nonconventional binary bismuth cuprate glasses of compositions (CuO)x(Bi2O3)100-x, for x = 27-70 mol %, prepared by the roller-quenching technique. It has been observed that stable glasses with nearly the same topology can be obtained in this system for a larger composition range compared to the multicomponent bismuth cuprate glasses. The network structure is built up of [BiO3] pyramidal units. The strength and connectivity of the glassy network increase at nearly equimolar glass composition. The nearly equimolar glass composition crystallizes to tetragonal Bi2CuO4 crystal. The appearance of hyperfine structure in the ESR line shapes for the glass compositions with high CuO content is not clear at this moment.